Sign

Returns the sign or parity of a permutation. It can be defined as the parity of pairs of elements $x,y$ such that $x<y$ and $\sigma \left(x\right)>\sigma \left(y\right)$. Thus, the sign is +1 is $\sigma$ is even or -1 if it is odd. Alternatively, the sign of a permutation can be defined from its decomposition into the product of transpositions as $(-1{)}^m$, where $m$ is the number of transpositions in the decomposition (although such decomposition is not unique, the parity is an invariant).

sign(Permutation)

Description

Given a permutation, returns its sign.